How to solve Linear Diophantine equations in programming?

Question

I have read about Linear Diophantine equations such as ax+by=c are called diophantine equations and give an integer solution only if gcd(a,b) divides c

Answer 1

Solving Linear Diophantine equations

ax + by = c and gcd(a, b) divides c.

1. Divide a, b and c by gcd(a,b).
2. Now gcd(a,b) == 1
3. Find solution to aU + bV = 1 using Extended Euclidean algorithm
4. Multiply equation by c. Now you have a(Uc) + b (Vc) = c
5. You found solution x = U*c and y = V * c